Dirac large numbers hypothesis

The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch.

[1] LNH was Dirac's personal response to a set of large number "coincidences" that had intrigued other theorists of his time.

The coincidence was further developed by Arthur Eddington (1931)[4] who related the above ratios to N, the estimated number of charged particles in the universe, with the following ratio:[5] In addition to the examples of Weyl and Eddington, Dirac was also influenced by the primeval-atom hypothesis of Georges Lemaître, who lectured on the topic in Cambridge in 1933.

The notion of a varying-G cosmology first appears in the work of Edward Arthur Milne a few years before Dirac formulated LNH.

Milne was inspired not by large number coincidences but by a dislike of Einstein's general theory of relativity.

The Weyl and Eddington ratios above can be rephrased in a variety of ways, as for instance in the context of time: where t is the age of the universe,

Although George Gamow noted that such a temporal variation does not necessarily follow from Dirac's assumptions,[8] a corresponding change of G has not been found.

Dirac met this difficulty by introducing into the Einstein field equations a gauge function β that describes the structure of spacetime in terms of a ratio of gravitational and electromagnetic units.

He also provided alternative scenarios for the continuous creation of matter, one of the other significant issues in LNH: Dirac's theory has inspired and continues to inspire a significant body of scientific literature in a variety of disciplines, with it sparking off many speculations, arguments and new ideas in terms of applications.

[10] In the context of geophysics, for instance, Edward Teller seemed to raise a serious objection to LNH in 1948[11] when he argued that variations in the strength of gravity are not consistent with paleontological data.

However, George Gamow demonstrated in 1962[12] how a simple revision of the parameters (in this case, the age of the Solar System) can invalidate Teller's conclusions.

This is for example the ratio of the theoretical and observational estimates of the energy density of the vacuum, which Nottale (1993)[18] and Matthews (1997)[19] associated in an LNH context with a scaling law for the cosmological constant.